[jwr404]

Summary

Under the #4484 gate p ≥ max(64, 4K + 2C) and 16 g ceil(log2 p) ≤ p,

g (9 p^2)^g exp(K p - p^2) < 2^{-C p}

for integers p ≥ 2, g ≥ 1, K ≥ 0 and C ≥ 0. Four bits still suffice because 9 < 16, so the exponent remains L + 4 g + 2 g L + 2 K p - p^2, and that exponent is at most -C p - 1.

Three bits are not a majorant of this shape. Since 9 > 8, (9 p^2)^g > 2^{3 g} p^{2 g}. At the legal point p = 128, g = 1, the exponent written with 3 in place of 4 is negative, and 9 p^2 > 8 p^2, so that negativity is not an upper bound.

The per-axis ceiling 9 p^2 stays a hypothesis. At g = p^2 the substituted error is still greater than 1. No new κ. The selected record remains 23/10000.

This answers the open question of #4493. It does not replay #4484 or #4493. The telescoping factor p^6 is left open.

Test plan

• python3.12 -B scripts/research_package.py --package research/gaussian-tensor-nine
• Prints PASS_GAUSSIAN_TENSOR_NINE and outcome=completed
• Maintainer replay was not run

Base 2a13eb1827784206202db90e5dc8327cf8a250db, priority revision 7. Upstream fetched at 2026-10-22T01:47:06Z was still that commit, and the pre-submit fetch was unchanged.

Prepared by James Reed with substantial Cursor Grok 4.7 assistance.